NZMATH  1.2.0 About: NZMATH is a Python based number theory oriented calculation system.   Fossies Dox: NZMATH-1.2.0.tar.gz  ("inofficial" and yet experimental doxygen-generated source code documentation)
nzmath.intresidue.IntegerResidueClassRing Class Reference
Inheritance diagram for nzmath.intresidue.IntegerResidueClassRing:
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## Public Member Functions

def __init__ (self, modulus)

def __repr__ (self)

def __str__ (self)

def __hash__ (self)

def card (self)

def getInstance (cls, modulus)

def createElement (self, seed)

def getCharacteristic (self)

def __contains__ (self, elem)

def isfield (self)

def __eq__ (self, other)

def __ne__ (self, other)

def issubring (self, other)

def issuperring (self, other)

Public Member Functions inherited from nzmath.ring.CommutativeRing
def __init__ (self)

def getQuotientField (self)

def isdomain (self)

def isnoetherian (self)

def isufd (self)

def ispid (self)

def iseuclidean (self)

def registerModuleAction (self, action_ring, action)

def hasaction (self, action_ring)

def getaction (self, action_ring)

Public Member Functions inherited from nzmath.ring.Ring
def getCommonSuperring (self, other)

## Public Attributes

m

Public Attributes inherited from nzmath.ring.CommutativeRing
properties

## Static Public Attributes

def isdomain = isfield

def isnoetherian = isfield

def isufd = isfield

def ispid = isfield

def iseuclidean = isfield

## Properties

one = property(_getOne, None, None, "multiplicative unit.")

zero = property(_getZero, None, None, "additive unit.")

## Private Member Functions

def _getOne (self)

def _getZero (self)

_one

_zero

## Static Private Attributes

dictionary _instances = {}

## Detailed Description

```IntegerResidueClassRing is also known as Z/mZ.
```

Definition at line 218 of file intresidue.py.

## ◆ __init__()

 def nzmath.intresidue.IntegerResidueClassRing.__init__ ( self, modulus )
```The argument modulus m specifies an ideal mZ.
```

Definition at line 225 of file intresidue.py.

## ◆ __contains__()

 def nzmath.intresidue.IntegerResidueClassRing.__contains__ ( self, elem )

Definition at line 277 of file intresidue.py.

## ◆ __eq__()

 def nzmath.intresidue.IntegerResidueClassRing.__eq__ ( self, other )
```Equality test.
```

Reimplemented from nzmath.ring.Ring.

Definition at line 302 of file intresidue.py.

## ◆ __hash__()

 def nzmath.intresidue.IntegerResidueClassRing.__hash__ ( self )

Reimplemented from nzmath.ring.Ring.

Definition at line 242 of file intresidue.py.

## ◆ __ne__()

 def nzmath.intresidue.IntegerResidueClassRing.__ne__ ( self, other )
```Inequality test.
```

Reimplemented from nzmath.ring.Ring.

Definition at line 307 of file intresidue.py.

## ◆ __repr__()

 def nzmath.intresidue.IntegerResidueClassRing.__repr__ ( self )

Definition at line 236 of file intresidue.py.

## ◆ __str__()

 def nzmath.intresidue.IntegerResidueClassRing.__str__ ( self )

Definition at line 239 of file intresidue.py.

## ◆ _getOne()

 def nzmath.intresidue.IntegerResidueClassRing._getOne ( self )
private

Definition at line 322 of file intresidue.py.

## ◆ _getZero()

 def nzmath.intresidue.IntegerResidueClassRing._getZero ( self )
private

Definition at line 330 of file intresidue.py.

## ◆ card()

 def nzmath.intresidue.IntegerResidueClassRing.card ( self )
```Return the cardinality of the ring.
```

Definition at line 245 of file intresidue.py.

## ◆ createElement()

 def nzmath.intresidue.IntegerResidueClassRing.createElement ( self, seed )
```createElement returns an element of the ring with seed.
```

Reimplemented from nzmath.ring.Ring.

Definition at line 263 of file intresidue.py.

## ◆ getCharacteristic()

 def nzmath.intresidue.IntegerResidueClassRing.getCharacteristic ( self )
```The characteristic of Z/mZ is m.
```

Reimplemented from nzmath.ring.Ring.

Definition at line 271 of file intresidue.py.

## ◆ getInstance()

 def nzmath.intresidue.IntegerResidueClassRing.getInstance ( cls, modulus )
```getInstance returns an instance of the class of specified
modulus.
```

Definition at line 252 of file intresidue.py.

## ◆ isfield()

 def nzmath.intresidue.IntegerResidueClassRing.isfield ( self )
```isfield returns True if the modulus is prime, False if not.
Since a finite domain is a field, other ring property tests
are merely aliases of isfield.
```

Reimplemented from nzmath.ring.CommutativeRing.

Definition at line 283 of file intresidue.py.

## ◆ issubring()

 def nzmath.intresidue.IntegerResidueClassRing.issubring ( self, other )
```Report whether another ring contains the ring as a subring.
```

Reimplemented from nzmath.ring.Ring.

Definition at line 310 of file intresidue.py.

## ◆ issuperring()

 def nzmath.intresidue.IntegerResidueClassRing.issuperring ( self, other )
```Report whether the ring is a superring of another ring.
```

Reimplemented from nzmath.ring.Ring.

Definition at line 316 of file intresidue.py.

## ◆ _instances

 dictionary nzmath.intresidue.IntegerResidueClassRing._instances = {}
staticprivate

## ◆ _one

 nzmath.intresidue.IntegerResidueClassRing._one
private

## ◆ _zero

 nzmath.intresidue.IntegerResidueClassRing._zero
private

## ◆ isdomain

 def nzmath.intresidue.IntegerResidueClassRing.isdomain = isfield
static

Definition at line 296 of file intresidue.py.

## ◆ iseuclidean

 def nzmath.intresidue.IntegerResidueClassRing.iseuclidean = isfield
static

Definition at line 300 of file intresidue.py.

## ◆ isnoetherian

 def nzmath.intresidue.IntegerResidueClassRing.isnoetherian = isfield
static

Definition at line 297 of file intresidue.py.

## ◆ ispid

 def nzmath.intresidue.IntegerResidueClassRing.ispid = isfield
static

Definition at line 299 of file intresidue.py.

## ◆ isufd

 def nzmath.intresidue.IntegerResidueClassRing.isufd = isfield
static

Definition at line 298 of file intresidue.py.

## ◆ one

 nzmath.intresidue.IntegerResidueClassRing.one = property(_getOne, None, None, "multiplicative unit.")
static

## ◆ zero

 nzmath.intresidue.IntegerResidueClassRing.zero = property(_getZero, None, None, "additive unit.")
static

Definition at line 336 of file intresidue.py.

Referenced by nzmath.ring.Field.gcd(), and nzmath.matrix.MatrixRing.zeroMatrix().

The documentation for this class was generated from the following file: